Turbine nozzle airfoil profile

ABSTRACT

The present application provides a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances may be joined smoothly with one another to form a complete airfoil shape.

TECHNICAL FIELD

The present application and the resultant patent relate generally to a turbine nozzle for a gas turbine engine and more particularly relate to a nozzle airfoil profile for a turbine stage.

BACKGROUND OF THE INVENTION

In a gas turbine, many system requirements should be met at each stage of the gas turbine so as to meet design goals. These design goals may include, but are not limited to, overall improved efficiency and airfoil loading capability. For example, a turbine nozzle airfoil profile should achieve thermal and mechanical operating requirements for that particular stage. Moreover, component lifetime and cost targets also should be met.

There is thus a desire therefore for an improved turbine nozzle airfoil profile for use in a turbine and the like. Such an improved airfoil design should achieve performance objectives and improve overall gas turbine performance in a component with a long lifetime and reasonable manufacture and operating costs.

SUMMARY OF THE INVENTION

The present application and the resultant patent thus provide a turbine nozzle including an airfoil shape. The airfoil shape may have a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z. The airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.

The present application and the resultant patent further provide a turbine nozzle including an airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete suction-side airfoil shape. The X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

The present application and the resultant patent further provide a turbine with a number of nozzles having an airfoil having an airfoil shape. The airfoils having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches. The X and Y values are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance. The airfoil profile sections at the Z distances may be joined smoothly with one another to form a complete airfoil shape.

These and other features and improvements of the present application and the resultant patent should become apparent to one of ordinary skill in the art upon review of the following detailed description when taken in conjunction with the several drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a gas turbine engine.

FIG. 2 is a schematic diagram of a portion of a turbine having a nozzle arrangement as may be described herein.

FIG. 3 is a perspective view of an airfoil as may be described herein.

FIG. 4 is a side cross-sectional view of the airfoil of FIG. 3.

DETAILED DESCRIPTION

Referring now to the drawings, in which like numerals refer to like elements throughout the several views, FIG. 1 shows a schematic view of gas turbine engine 10 as may be used herein. The gas turbine engine 10 may include a compressor 15. The compressor 15 compresses an incoming flow of air 20. The compressor 15 delivers the compressed flow of air 20 to a combustor 25. The combustor 25 mixes the compressed flow of air 20 with a pressurized flow of fuel 30 and ignites the mixture to create a flow of combustion gases 35. Although only a single combustor 25 is shown, the gas turbine engine 10 may include any number of combustors 25. The flow of combustion gases 35 is in turn delivered to a turbine 40. The flow of combustion gases 35 drives the turbine 40 so as to produce mechanical work. The mechanical work produced in the turbine 40 drives the compressor 15 via a shaft 45 and an external load 50 such as an electrical generator and the like.

The gas turbine engine 10 may use natural gas, various types of syngas, and/or other types of fuels. The gas turbine engine 10 may be any one of a number of different gas turbine engines offered by General Electric Company of Schenectady, N.Y., including, but not limited to, those such as a 7 or a 9 series heavy duty gas turbine engine and the like. The gas turbine engine 10 may have different configurations and may use other types of components. Other types of gas turbine engines also may be used herein. Multiple gas turbine engines, other types of turbines, and other types of power generation equipment also may be used herein together.

FIG. 2 shows a schematic diagram of a turbine 100 as may be described herein. The turbine 100 may include a first stage 110, a second stage 120, a third stage 130, a fourth stage 140, a fifth stage 142, a sixth stage 144, and the like. Any number of stages may be used herein. For example, the first stage 110 may include a number of circumferentially spaced nozzles 150 and buckets 160. The first stage buckets 160 are mounted on a turbine rotor 170. The nozzles 150 are circumferentially spaced one from the other and fixed about an axis of the rotor. The second stage of the turbine 100 includes a number of circumferentially spaced nozzles 180 and a number of circumferentially spaced buckets 190 mounted on the rotor 170. The third stage also includes a number of circumferentially spaced nozzles 200 and buckets 210 mounted on the rotor 170. The fourth stage 140 includes a number of circumferentially spaced nozzles 220 and buckets 230 mounted on the rotor 170. The fifth stage 142 includes a number of circumferentially spaced nozzles 232 and buckets 234 mounted on the rotor 170. The sixth stage 144 includes a number of circumferentially spaced nozzles 236 and buckets 238 mounted on the rotor 170. Again, any number of stages may be used herein. It will be appreciated that the nozzles and buckets lie in a hot gas path 240 of the turbine. Other components and other configurations may be used herein.

Referring to FIG. 3 and FIG. 4, it will be appreciated that each nozzle 220 has a nozzle airfoil 250 as illustrated. The airfoil 250 may have a suction side 260 and a pressure side 270. The suction side 260 is shown in FIG. 4 and the pressure side 270 is located on the opposing side of the airfoil 250. Thus, each of the nozzles 220 has a nozzle airfoil profile at any cross-section in the shape of the airfoil 250. A tip 280 is at or near the top of the airfoil 250 and a base 290 is at or near the bottom of the airfoil 250. The airfoil 250 also includes a leading edge 300, a trailing edge 310, and a chord length 320 therebetween. The base 290 corresponds to the non-dimensional Z value of Table 1 at Z equals 0. The tip 280 of the nozzle airfoil 250 corresponds to the non-dimensional Z value of Table 1 at Z equals 100. The X, Y, and Z values are given in percentage values of the airfoil length. As one example only, the height of the turbine nozzle or airfoil 250 may be from about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters), However, it is to be understood that heights below or above this range may also be employed as desired in the specific application. The airfoil 250 may be used for any stage, including but not limited to a first stage, a second stage, a third stage, a fourth stage, a fifth stage, and the like.

The gas turbine hot gas path 240 requires airfoils 250 that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each nozzle airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to run in an efficient, safe and smooth manner. These points are unique and specific to the system. The locus that defines the nozzle airfoil profile includes a set of about 2,200 points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in Table 1 below defines the profile of the nozzle airfoil at various locations along its length. Table 1 lists data for a non-coated airfoil. The envelope/tolerance for the coordinates is about +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord length 320 in a direction nominal to any airfoil surface location. The point data origin is the leading edge of the base 290. The coordinate values for the X, Y and Z coordinates are set forth in non-dimensionalized units by the blade height in Table 1 although other units of dimensions may be used when the values are appropriately converted. The X, Y, and Z values set forth in Table 1 are also expressed in non-dimensional form (X, Y, and Z) from 0% to 100% of the blade or airfoil height. As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a height of the airfoil at the trailing edge and multiplying by a constant number (e.g., 100). To convert the Z value to a Z coordinate value, e.g., in inches, the non-dimensional Z value given in Table 1 is multiplied by the Z length of the airfoil in inches. As described above, the Cartesian coordinate system has orthogonally-related X, Y and Z axes and the X axis lies generally parallel to the turbine rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the nozzle tip. All the values in Table 1 are given at room temperature and are unfilleted.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, the profile section or airfoil shape of the nozzle airfoil, at each Z distance along the length of the airfoil can be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each distance Z is fixed. The airfoil profiles of the various surface locations between the distances Z are determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The Table 1 values are generated and shown to three decimal places for determining the profile of the airfoil. As the blade heats up in surface, stress and temperature will cause a change in the X, Y and Z values. Accordingly, the values for the profile given in Table 1 represent ambient, non-operating or non-hot conditions (e.g., room temperature) and are for an uncoated airfoil.

There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil. Each section is joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in Table 1 below. Accordingly, a distance of +/−5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular nozzle airfoil design and turbine, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the Table below at the same temperature. The data is scalable and the geometry pertains to all aerodynamic scales, at above and/or below 3000 RPM. The nozzle airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

TABLE 1 N Location X Y Z 1 Suction-Side 0.000 0.000 0 2 Suction-Side −0.041 −0.434 0 3 Suction-Side −0.032 −0.869 0 4 Suction-Side 0.037 −1.299 0 5 Suction-Side 0.176 −1.710 0 6 Suction-Side 0.387 −2.091 0 7 Suction-Side 0.660 −2.430 0 8 Suction-Side 0.981 −2.724 0 9 Suction-Side 1.337 −2.975 0 10 Suction-Side 1.716 −3.189 0 11 Suction-Side 2.112 −3.370 0 12 Suction-Side 2.520 −3.524 0 13 Suction-Side 2.936 −3.654 0 14 Suction-Side 3.357 −3.763 0 15 Suction-Side 3.784 −3.852 0 16 Suction-Side 4.214 −3.923 0 17 Suction-Side 4.646 −3.977 0 18 Suction-Side 5.080 −4.016 0 19 Suction-Side 5.515 −4.039 0 20 Suction-Side 5.950 −4.047 0 21 Suction-Side 6.386 −4.041 0 22 Suction-Side 6.821 −4.021 0 23 Suction-Side 7.255 −3.988 0 24 Suction-Side 7.688 −3.939 0 25 Suction-Side 8.120 −3.878 0 26 Suction-Side 8.548 −3.802 0 27 Suction-Side 8.975 −3.714 0 28 Suction-Side 9.399 −3.611 0 29 Suction-Side 9.819 −3.496 0 30 Suction-Side 10.235 −3.367 0 31 Suction-Side 10.647 −3.224 0 32 Suction-Side 11.053 −3.069 0 33 Suction-Side 11.455 −2.900 0 34 Suction-Side 11.851 −2.719 0 35 Suction-Side 12.241 −2.524 0 36 Suction-Side 12.624 −2.317 0 37 Suction-Side 13.000 −2.098 0 38 Suction-Side 13.369 −1.867 0 39 Suction-Side 13.731 −1.624 0 40 Suction-Side 14.085 −1.370 0 41 Suction-Side 14.431 −1.105 0 42 Suction-Side 14.770 −0.831 0 43 Suction-Side 15.100 −0.547 0 44 Suction-Side 15.422 −0.253 0 45 Suction-Side 15.736 0.049 0 46 Suction-Side 16.042 0.358 0 47 Suction-Side 16.341 0.675 0 48 Suction-Side 16.633 0.999 0 49 Suction-Side 16.917 1.329 0 50 Suction-Side 17.194 1.665 0 51 Suction-Side 17.465 2.006 0 52 Suction-Side 17.729 2.353 0 53 Suction-Side 17.988 2.703 0 54 Suction-Side 18.241 3.058 0 55 Suction-Side 18.489 3.416 0 56 Suction-Side 18.731 3.778 0 57 Suction-Side 18.969 4.143 0 58 Suction-Side 19.203 4.510 0 59 Suction-Side 19.433 4.881 0 60 Suction-Side 19.658 5.253 0 61 Suction-Side 19.880 5.628 0 62 Suction-Side 20.099 6.005 0 63 Suction-Side 20.315 6.384 0 64 Suction-Side 20.528 6.764 0 65 Suction-Side 20.738 7.145 0 66 Suction-Side 20.945 7.528 0 67 Suction-Side 21.151 7.913 0 68 Suction-Side 21.354 8.298 0 69 Suction-Side 21.555 8.684 0 70 Suction-Side 21.754 9.072 0 71 Suction-Side 21.952 9.460 0 72 Suction-Side 22.148 9.849 0 73 Suction-Side 22.342 10.239 0 74 Suction-Side 22.535 10.630 0 75 Suction-Side 22.727 11.020 0 76 Suction-Side 22.918 11.412 0 77 Suction-Side 23.107 11.804 0 78 Suction-Side 23.296 12.197 0 79 Suction-Side 23.484 12.590 0 80 Suction-Side 23.670 12.984 0 81 Suction-Side 23.856 13.378 0 82 Suction-Side 24.041 13.772 0 83 Suction-Side 24.226 14.167 0 84 Suction-Side 24.410 14.562 0 85 Suction-Side 24.593 14.957 0 86 Suction-Side 24.775 15.353 0 87 Suction-Side 24.957 15.748 0 88 Suction-Side 25.139 16.144 0 89 Suction-Side 25.320 16.541 0 90 Suction-Side 25.501 16.937 0 91 Suction-Side 25.681 17.334 0 92 Suction-Side 25.861 17.730 0 93 Suction-Side 26.040 18.128 0 94 Suction-Side 26.220 18.525 0 95 Suction-Side 26.399 18.922 0 96 Suction-Side 26.577 19.319 0 97 Suction-Side 26.755 19.717 0 98 Suction-Side 26.934 20.114 0 99 Suction-Side 77.112 70.512 0 100 Suction-Side 27.289 20.909 0 101 Pressure-Side 27.202 21.276 0 102 Pressure-Side 26.911 21.126 0 103 Pressure-Side 26.728 20.811 0 104 Pressure-Side 26.545 20.497 0 105 Pressure-Side 26.361 20.183 0 106 Pressure-Side 26.176 19.869 0 107 Pressure-Side 25.991 19.556 0 108 Pressure-Side 25.805 19.243 0 109 Pressure-Side 25.618 18.931 0 110 Pressure-Side 25.430 18.619 0 111 Pressure-Side 25.241 18.308 0 112 Pressure-Side 25.051 17.998 0 113 Pressure-Side 24.860 17.688 0 114 Pressure-Side 24.668 17.379 0 115 Pressure-Side 24.475 17.070 0 116 Pressure-Side 24.280 16.763 0 117 Pressure-Side 24.085 16.456 0 118 Pressure-Side 23.888 16.150 0 119 Pressure-Side 23.690 15.845 0 120 Pressure-Side 23.491 15.540 0 121 Pressure-Side 23.290 15.236 0 122 Pressure-Side 23.089 14.933 0 123 Pressure-Side 22.886 14.630 0 124 Pressure-Side 22.682 14.329 0 125 Pressure-Side 22.477 14.029 0 126 Pressure-Side 22.270 13.729 0 127 Pressure-Side 22.062 13.430 0 128 Pressure-Side 21.853 13.133 0 129 Pressure-Side 21.642 12.836 0 130 Pressure-Side 21.429 12.541 0 131 Pressure-Side 21.214 12.247 0 132 Pressure-Side 20.998 11.955 0 133 Pressure-Side 20.779 11.663 0 134 Pressure-Side 20.559 11.374 0 135 Pressure-Side 20.336 11.086 0 136 Pressure-Side 20.111 10.800 0 137 Pressure-Side 19.883 10.516 0 138 Pressure-Side 19.653 10.234 0 139 Pressure-Side 19.420 9.955 0 140 Pressure-Side 19.184 9.678 0 141 Pressure-Side 18.945 9.403 0 142 Pressure-Side 18.703 9.131 0 143 Pressure-Side 18.458 8.862 0 144 Pressure-Side 18.209 8.597 0 145 Pressure-Side 17.957 8.334 0 146 Pressure-Side 17.702 8.075 0 147 Pressure-Side 17.442 7.819 0 148 Pressure-Side 17.179 7.568 0 149 Pressure-Side 16.913 7.319 0 150 Pressure-Side 16.643 7.076 0 151 Pressure-Side 16.369 6.836 0 152 Pressure-Side 16.091 6.601 0 153 Pressure-Side 15.809 6.371 0 154 Pressure-Side 15.524 6.145 0 155 Pressure-Side 15.235 5.924 0 156 Pressure-Side 14.942 5.708 0 157 Pressure-Side 14.645 5.497 0 158 Pressure-Side 14.345 5.292 0 159 Pressure-Side 14.041 5.091 0 160 Pressure-Side 13.733 4.896 0 161 Pressure-Side 13.422 4.708 0 162 Pressure-Side 13.108 4.524 0 163 Pressure-Side 12.790 4.346 0 164 Pressure-Side 12.470 4.174 0 165 Pressure-Side 12.146 4.008 0 166 Pressure-Side 11.819 3.847 0 167 Pressure-Side 11.490 3.693 0 168 Pressure-Side 11.158 3.544 0 169 Pressure-Side 10.823 3.401 0 170 Pressure-Side 10.486 3.264 0 171 Pressure-Side 10.146 3.133 0 172 Pressure-Side 9.804 3.008 0 173 Pressure-Side 9.461 2.888 0 174 Pressure-Side 9.115 2.774 0 175 Pressure-Side 8.768 2.666 0 176 Pressure-Side 8.419 2.562 0 177 Pressure-Side 8.068 2.465 0 178 Pressure-Side 7.716 2.372 0 179 Pressure-Side 7.363 2.284 0 180 Pressure-Side 7.009 2.201 0 181 Pressure-Side 6.653 2.123 0 182 Pressure-Side 6.297 2.048 0 183 Pressure-Side 5.940 1.978 0 184 Pressure-Side 5.582 1.912 0 185 Pressure-Side 5.224 1.848 0 186 Pressure-Side 4.865 1.788 0 187 Pressure-Side 4.505 1.730 0 188 Pressure-Side 4.146 1.673 0 189 Pressure-Side 3.786 1.618 0 190 Pressure-Side 3.426 1.563 0 191 Pressure-Side 3.067 1.508 0 192 Pressure-Side 2.707 1.450 0 193 Pressure-Side 2.349 1.388 0 194 Pressure-Side 1.991 1.318 0 195 Pressure-Side 1.637 1.238 0 196 Pressure-Side 1.286 1.141 0 197 Pressure-Side 0.943 1.018 0 198 Pressure-Side 0.618 0.856 0 199 Pressure-Side 0.329 0.635 0 200 Pressure-Side 0.113 0.344 0 1 Suction-Side −0.494 −0.520 10 2 Suction-Side −0.528 −0.961 10 3 Suction-Side −0.492 −1.401 10 4 Suction-Side −0.383 −1.829 10 5 Suction-Side −0.200 −2.232 10 6 Suction-Side 0.047 −2.598 10 7 Suction-Side 0.346 −2.924 10 8 Suction-Side 0.684 −3.208 10 9 Suction-Side 1.052 −3.454 10 10 Suction-Side 1.440 −3.665 10 11 Suction-Side 1.844 −3.846 10 12 Suction-Side 2.260 −3.998 10 13 Suction-Side 2.684 −4.124 10 14 Suction-Side 3.114 −4.228 10 15 Suction-Side 3.548 −4.310 10 16 Suction-Side 3.987 −4.372 10 17 Suction-Side 4.427 −4.415 10 18 Suction-Side 4.868 −4.441 10 19 Suction-Side 5.311 −4.451 10 20 Suction-Side 5.753 −4.444 10 21 Suction-Side 6.195 −4.423 10 22 Suction-Side 6.636 −4.387 10 23 Suction-Side 7.075 −4.337 10 24 Suction-Side 7.513 −1.273 10 25 Suction-Side 7.949 −4.195 10 26 Suction-Side 8.382 −4.105 10 27 Suction-Side 8.812 −4.002 10 28 Suction-Side 9.239 −3.886 10 29 Suction-Side 9.662 −3.758 10 30 Suction-Side 10.081 −3.617 10 31 Suction-Side 10.497 −3.464 10 32 Suction-Side 10.907 −3.299 10 33 Suction-Side 11.312 −3.122 10 34 Suction-Side 11.712 −2.933 10 35 Suction-Side 12.107 −2.732 10 36 Suction-Side 12.495 −2.521 10 37 Suction-Side 12.877 −2.298 10 38 Suction-Side 13.253 −2.064 10 39 Suction-Side 13.622 −1.820 10 40 Suction-Side 13.984 −1.565 10 41 Suction-Side 14.339 −1.301 10 42 Suction-Side 14.686 −1.028 10 43 Suction-Side 15.026 −0.745 10 44 Suction-Side 15.359 −0.453 10 45 Suction-Side 15.685 −0.154 10 46 Suction-Side 16.003 0.153 10 47 Suction-Side 16.314 0.468 10 48 Suction-Side 16.618 0.789 10 49 Suction-Side 16.916 1.117 10 50 Suction-Side 17.206 1.450 10 51 Suction-Side 17.491 1.789 10 52 Suction-Side 17.768 2.134 10 53 Suction-Side 18.041 2.482 10 54 Suction-Side 18.307 2.835 10 55 Suction-Side 18.569 3.192 10 56 Suction-Side 18.825 3.552 10 57 Suction-Side 19.077 3.916 10 58 Suction-Side 19.324 4.284 10 59 Suction-Side 19.567 4.653 10 60 Suction-Side 19.806 5.025 10 61 Suction-Side 20.041 5.400 10 62 Suction-Side 20.273 5.777 10 63 Suction-Side 20.502 6.156 10 64 Suction-Side 20.728 6.536 10 65 Suction-Side 20.950 6.918 10 66 Suction-Side 21.170 7.302 10 67 Suction-Side 21.388 7.687 10 68 Suction-Side 21.603 8.074 10 69 Suction-Side 21.817 8.461 10 70 Suction-Side 22.028 8.850 10 71 Suction-Side 22.237 9.240 10 72 Suction-Side 22.445 9.630 10 73 Suction-Side 22.651 10.021 10 74 Suction-Side 22.856 10.414 10 75 Suction-Side 23.060 10.807 10 76 Suction-Side 23.262 11.200 10 77 Suction-Side 23.463 11.594 10 78 Suction-Side 23.663 11.989 10 79 Suction-Side 23.863 12.383 10 80 Suction-Side 24.061 12.779 10 81 Suction-Side 24.258 13.175 10 82 Suction-Side 24.455 13.571 10 83 Suction-Side 24.651 13.968 10 84 Suction-Side 24.846 14.365 10 85 Suction-Side 25.041 14.762 10 86 Suction-Side 25.235 15.160 10 87 Suction-Side 25.428 15.558 10 88 Suction-Side 25.621 15.956 10 89 Suction-Side 25.814 16.354 10 90 Suction-Side 26.006 16.752 10 91 Suction-Side 26.198 17.151 10 92 Suction-Side 26.390 17.550 10 93 Suction-Side 26.581 17.949 10 94 Suction-Side 26.772 18.348 10 95 Suction-Side 26.963 18.747 10 96 Suction-Side 27.153 19.146 10 97 Suction-Side 27.343 19.546 10 98 Suction-Side 27.533 19.945 10 99 Suction-Side 27.722 20.345 10 100 Suction-Side 27.911 20.745 10 101 Pressure-Side 27.830 21.117 10 102 Pressure-Side 27.531 20.963 10 103 Pressure-Side 27.336 20.644 10 104 Pressure-Side 27.141 20.324 10 105 Pressure-Side 26.944 20.006 10 106 Pressure-Side 26.748 19.687 10 107 Pressure-Side 26.550 19.369 10 108 Pressure-Side 26.352 19.051 10 109 Pressure-Side 26.154 18.734 10 110 Pressure-Side 25.954 18.417 10 111 Pressure-Side 25.754 18.100 10 112 Pressure-Side 25.554 17.785 10 113 Pressure-Side 25.352 17.469 10 114 Pressure-Side 25.150 17.154 10 115 Pressure-Side 24.947 16.840 10 116 Pressure-Side 24.742 16.526 10 117 Pressure-Side 24.537 16.212 10 118 Pressure-Side 24.331 15.900 10 119 Pressure-Side 24.125 15.588 10 120 Pressure-Side 23.916 15.277 10 121 Pressure-Side 23.707 14.966 10 122 Pressure-Side 23.497 14.656 10 123 Pressure-Side 23.286 14.348 10 124 Pressure-Side 23.073 14.039 10 125 Pressure-Side 22.858 13.733 10 126 Pressure-Side 22.643 13.427 10 127 Pressure-Side 22.425 13.122 10 128 Pressure-Side 22.206 12.819 10 129 Pressure-Side 21.984 12.517 10 130 Pressure-Side 21.761 12.216 10 131 Pressure-Side 21.536 11.917 10 132 Pressure-Side 21.308 11.620 10 133 Pressure-Side 21.077 11.325 10 134 Pressure-Side 20.844 11.032 10 135 Pressure-Side 20.609 10.741 10 136 Pressure-Side 20.370 10.453 10 137 Pressure-Side 20.128 10.168 10 138 Pressure-Side 19.883 9.885 10 139 Pressure-Side 19.634 9.604 10 140 Pressure-Side 19.382 9.327 10 141 Pressure-Side 19.127 9.054 10 142 Pressure-Side 18.868 8.783 10 143 Pressure-Side 18.605 8.516 10 144 Pressure-Side 18.339 8.254 10 145 Pressure-Side 18.069 7.994 10 146 Pressure-Side 17.795 7.739 10 147 Pressure-Side 17.517 7.488 10 148 Pressure-Side 17.236 7.241 10 149 Pressure-Side 16.950 6.999 10 150 Pressure-Side 16.661 6.761 10 151 Pressure-Side 16.369 6.527 10 152 Pressure-Side 16.073 6.298 10 153 Pressure-Side 15.773 6.074 10 154 Pressure-Side 15.470 5.854 10 155 Pressure-Side 15.163 5.640 10 156 Pressure-Side 14.853 5.430 10 157 Pressure-Side 14.540 5.224 10 158 Pressure-Side 14.223 5.025 10 159 Pressure-Side 13.904 4.829 10 160 Pressure-Side 13.582 4.639 10 161 Pressure-Side 13.256 4.454 10 162 Pressure-Side 12.928 4.274 10 163 Pressure-Side 12.596 4.100 10 164 Pressure-Side 12.262 3.931 10 165 Pressure-Side 11.926 3.767 10 166 Pressure-Side 11.586 3.609 10 167 Pressure-Side 11.244 3.457 10 168 Pressure-Side 10.900 3.310 10 169 Pressure-Side 10.553 3.169 10 170 Pressure-Side 10.204 3.034 10 171 Pressure-Side 9.853 2.905 10 172 Pressure-Side 9.499 2.781 10 173 Pressure-Side 9.144 2.664 10 174 Pressure-Side 8.787 2.552 10 175 Pressure-Side 8.428 2.445 10 176 Pressure-Side 8.067 2.345 10 177 Pressure-Side 7.705 2.250 10 178 Pressure-Side 7.342 2.160 10 179 Pressure-Side 6.977 2.075 10 180 Pressure-Side 6.611 1.995 10 181 Pressure-Side 6.245 1.919 10 182 Pressure-Side 5.877 1.847 10 183 Pressure-Side 5.509 1.779 10 184 Pressure-Side 5.141 1.713 10 185 Pressure-Side 4.772 1.649 10 186 Pressure-Side 4.403 1.587 10 187 Pressure-Side 4.033 1.525 10 188 Pressure-Side 3.664 1.463 10 189 Pressure-Side 3.296 1.399 10 190 Pressure-Side 2.927 1.333 10 191 Pressure-Side 2.559 1.262 10 192 Pressure-Side 2.193 1.185 10 193 Pressure-Side 1.829 1.099 10 194 Pressure-Side 1.467 1.003 10 195 Pressure-Side 1.110 0.890 10 196 Pressure-Side 0.760 0.757 10 197 Pressure-Side 0.422 0.595 10 198 Pressure-Side 0.107 0.394 10 199 Pressure-Side −0.170 0.144 10 200 Pressure-Side −0.380 −0.165 10 1 Suction-Side −0.986 −1.035 20 2 Suction-Side −1.006 −1.484 20 3 Suction-Side −0.937 −1.927 20 4 Suction-Side −0.788 −2.351 20 5 Suction-Side −0.568 −2.743 20 6 Suction-Side −0.291 −3.097 20 7 Suction-Side 0.030 −3.412 20 8 Suction-Side 0.385 −3.688 20 9 Suction-Side 0.764 −3.929 20 10 Suction-Side 1.163 −4.136 20 11 Suction-Side 1.577 −4.312 20 12 Suction-Side 2.002 −4.460 20 13 Suction-Side 2.435 −4.582 20 14 Suction-Side 2.874 −4.679 20 15 Suction-Side 3.318 −4.754 20 16 Suction-Side 3.764 −4.808 20 17 Suction-Side 4.213 −4.842 20 18 Suction-Side 4.662 −4.858 20 19 Suction-Side 5.112 −4.857 20 20 Suction-Side 5.562 −4.840 20 21 Suction-Side 6.010 −4.807 20 22 Suction-Side 6.457 −4.759 20 23 Suction-Side 6.903 −4.697 20 24 Suction-Side 7.346 −4.621 20 25 Suction-Side 7.787 −4.532 20 26 Suction-Side 8.226 −4.431 20 27 Suction-Side 8.661 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Pressure-Side −1.603 −1.308 70 195 Pressure-Side −1.980 −1.533 70 196 Pressure-Side −2.340 −1.784 70 197 Pressure-Side −2.675 −2.066 70 198 Pressure-Side −2.973 −2.389 70 199 Pressure-Side −3.213 −2.756 70 200 Pressure-Side −3.369 −3.165 70 1 Suction-Side −3.899 −4.116 80 2 Suction-Side −3.795 −4.608 80 3 Suction-Side −3.554 −5.050 80 4 Suction-Side −3.219 −5.427 80 5 Suction-Side −2.828 −5.745 80 6 Suction-Side −2.401 −6.014 80 7 Suction-Side −1.951 −6.243 80 8 Suction-Side −1.484 −6.437 80 9 Suction-Side −1.007 −6.602 80 10 Suction-Side −0.522 −6.741 80 11 Suction-Side −0.030 −6.857 80 12 Suction-Side 0.466 −6.952 80 13 Suction-Side 0.965 −7.027 80 14 Suction-Side 1.467 −7.083 80 15 Suction-Side 1.970 −7.123 80 16 Suction-Side 2.475 −7.147 80 17 Suction-Side 2.979 −7.156 80 18 Suction-Side 3.484 −7.149 80 19 Suction-Side 3.989 −7.129 80 20 Suction-Side 4.493 −7.095 80 21 Suction-Side 4.996 −7.049 80 22 Suction-Side 5.497 −6.990 80 23 Suction-Side 5.997 −6.919 80 24 Suction-Side 6.495 −6.838 80 25 Suction-Side 6.992 −6.744 80 26 Suction-Side 7.486 −6.640 80 27 Suction-Side 7.978 −6.525 80 28 Suction-Side 8.467 −6.400 80 29 Suction-Side 8.953 −6.264 80 30 Suction-Side 9.436 −6.118 80 31 Suction-Side 9.917 −5.962 80 32 Suction-Side 10.394 −5.796 80 33 Suction-Side 10.867 −5.619 80 34 Suction-Side 11.336 −5.433 80 35 Suction-Side 11.802 −5.237 80 36 Suction-Side 12.263 −5.032 80 37 Suction-Side 12.720 −4.816 80 38 Suction-Side 13.172 −4.591 80 39 Suction-Side 13.619 −4.357 80 40 Suction-Side 14.061 −4.113 80 41 Suction-Side 14.498 −3.860 80 42 Suction-Side 14.930 −3.599 80 43 Suction-Side 15.356 −3.328 80 44 Suction-Side 15.777 −3.049 80 45 Suction-Side 16.192 −2.761 80 46 Suction-Side 16.602 −2.465 80 47 Suction-Side 17.405 −2.161 80 48 Suction-Side 17.402 −1.850 80 49 Suction-Side 17.794 −1.531 80 50 Suction-Side 18.180 −1.205 80 51 Suction-Side 18.560 −0.872 80 52 Suction-Side 18.933 −0.532 80 53 Suction-Side 19.301 −0.186 80 54 Suction-Side 19.663 0.166 80 55 Suction-Side 20.019 0.524 80 56 Suction-Side 20.370 0.887 80 57 Suction-Side 20.715 1.256 80 58 Suction-Side 21.055 1.629 80 59 Suction-Side 21.389 2.008 80 60 Suction-Side 21.718 2.391 80 61 Suction-Side 22.042 2.778 80 62 Suction-Side 22.362 3.169 80 63 Suction-Side 22.676 3.564 80 64 Suction-Side 22.986 3.963 80 65 Suction-Side 23.292 4.365 80 66 Suction-Side 23.593 4.770 80 67 Suction-Side 23.890 5.179 80 68 Suction-Side 24.183 5.590 80 69 Suction-Side 24.473 6.004 80 70 Suction-Side 24.758 6.420 80 71 Suction-Side 25.040 6.839 80 72 Suction-Side 25.319 7.260 80 73 Suction-Side 25.594 7.683 80 74 Suction-Side 25.867 8.109 80 75 Suction-Side 26.136 8.536 80 76 Suction-Side 26.403 8.965 80 77 Suction-Side 26.667 9.395 80 78 Suction-Side 26.929 9.827 80 79 Suction-Side 27.188 10.260 80 80 Suction-Side 27.445 10.695 80 81 Suction-Side 27.699 11.131 80 82 Suction-Side 27.952 11.569 80 83 Suction-Side 28.203 12.007 80 84 Suction-Side 28.452 12.446 80 85 Suction-Side 28.699 12.887 80 86 Suction-Side 28.945 13.328 80 87 Suction-Side 29.189 13.770 80 88 Suction-Side 29.432 14.212 80 89 Suction-Side 29.674 14.656 80 90 Suction-Side 29.914 15.100 80 91 Suction-Side 30.153 15.545 80 92 Suction-Side 30.392 15.990 80 93 Suction-Side 30.629 16.435 80 94 Suction-Side 30.866 16.882 80 95 Suction-Side 31.101 17.328 80 96 Suction-Side 31.337 17.775 80 97 Suction-Side 31.571 18.222 80 98 Suction-Side 31.804 18.671 80 99 Suction-Side 32.037 19.118 80 100 Suction-Side 32.269 19.567 80 101 Pressure-Side 32.222 19.995 80 102 Pressure-Side 31.883 19.769 80 103 Pressure-Side 31.635 19.393 80 104 Pressure-Side 31.386 19.019 80 105 Pressure-Side 31.134 18.645 80 106 Pressure-Side 30.880 18.273 80 107 Pressure-Side 30.624 17.903 80 108 Pressure-Side 30.366 17.534 80 109 Pressure-Side 30.104 17.166 80 110 Pressure-Side 29.841 16.801 80 111 Pressure-Side 29.574 16.439 80 112 Pressure-Side 29.305 16.077 80 113 Pressure-Side 29.033 15.718 80 114 Pressure-Side 28.758 15.362 80 115 Pressure-Side 28.479 15.008 80 116 Pressure-Side 28.197 14.657 80 117 Pressure-Side 27.912 14.308 80 118 Pressure-Side 27.623 13.963 80 119 Pressure-Side 27.331 13.620 80 120 Pressure-Side 27.035 13.281 80 121 Pressure-Side 26.735 12.945 80 122 Pressure-Side 26.431 12.612 80 123 Pressure-Side 26.124 12.283 80 124 Pressure-Side 25.813 11.957 80 125 Pressure-Side 25.498 11.635 80 126 Pressure-Side 25.179 11.317 80 127 Pressure-Side 24.856 11.003 80 128 Pressure-Side 24.529 10.693 80 129 Pressure-Side 24.199 10.387 80 130 Pressure-Side 23.864 10.086 80 131 Pressure-Side 23.526 9.788 80 132 Pressure-Side 23.184 9.495 80 133 Pressure-Side 22.838 9.206 80 134 Pressure-Side 22.489 8.922 80 135 Pressure-Side 22.136 8.643 80 136 Pressure-Side 21.780 8.367 80 137 Pressure-Side 21.420 8.096 80 138 Pressure-Side 21.057 7.830 80 139 Pressure-Side 20.691 7.568 80 140 Pressure-Side 20.321 7.310 80 141 Pressure-Side 19.949 7.057 80 142 Pressure-Side 19.573 6.809 80 143 Pressure-Side 19.194 6.565 80 144 Pressure-Side 18.813 6.325 80 145 Pressure-Side 18.429 6.090 80 146 Pressure-Side 18.042 5.860 80 147 Pressure-Side 17.652 5.633 80 148 Pressure-Side 17.261 5.411 80 149 Pressure-Side 16.866 5.194 80 150 Pressure-Side 16.469 4.981 80 151 Pressure-Side 16.070 4.772 80 152 Pressure-Side 15.669 4.567 80 153 Pressure-Side 15.266 4.367 80 154 Pressure-Side 14.860 4.171 80 155 Pressure-Side 14.453 3.979 80 156 Pressure-Side 14.043 3.791 80 157 Pressure-Side 13.632 3.608 80 158 Pressure-Side 13.218 3.429 80 159 Pressure-Side 12.804 3.254 80 160 Pressure-Side 12.387 3.083 80 161 Pressure-Side 11.968 2.916 80 162 Pressure-Side 11.549 2.753 80 163 Pressure-Side 11.127 2.594 80 164 Pressure-Side 10.704 2.440 80 165 Pressure-Side 10.280 2.289 80 166 Pressure-Side 9.854 2.142 80 167 Pressure-Side 9.427 1.998 80 168 Pressure-Side 8.999 1.857 80 169 Pressure-Side 8.570 1.721 80 170 Pressure-Side 8.140 1.587 80 171 Pressure-Side 7.709 1.457 80 172 Pressure-Side 7.277 1.329 80 173 Pressure-Side 6.844 1.205 80 174 Pressure-Side 6.411 1.082 80 175 Pressure-Side 5.977 0.961 80 176 Pressure-Side 5.543 0.843 80 177 Pressure-Side 5.108 0.725 80 178 Pressure-Side 4.673 0.608 80 179 Pressure-Side 4.238 0.492 80 180 Pressure-Side 3.803 0.376 80 181 Pressure-Side 3.367 0.259 80 182 Pressure-Side 2.933 0.141 80 183 Pressure-Side 2.499 0.021 80 184 Pressure-Side 2.065 −0.101 80 185 Pressure-Side 1.633 −0.227 80 186 Pressure-Side 1.202 −0.357 80 187 Pressure-Side 0.772 −0.492 80 188 Pressure-Side 0.345 −0.633 80 189 Pressure-Side −0.081 −0.782 80 190 Pressure-Side −0.502 −0.940 80 191 Pressure-Side −0.920 −1.109 80 192 Pressure-Side −1.332 −1.291 80 193 Pressure-Side −1.737 −1.488 80 194 Pressure-Side −2.132 −1.703 80 195 Pressure-Side −2.514 −1.942 80 196 Pressure-Side −2.877 −2.208 80 197 Pressure-Side −3.212 −2.510 80 198 Pressure-Side −3.503 −2.852 80 199 Pressure-Side −3.731 −3.240 80 200 Pressure-Side −3.869 −3.668 80 1 Suction-Side −4.378 −4.636 90 2 Suction-Side −4.255 −5.135 90 3 Suction-Side −3.984 −5.571 90 4 Suction-Side −3.618 −5.933 90 5 Suction-Side −3.198 −6.231 90 6 Suction-Side −2.745 −6.478 90 7 Suction-Side −2.273 −6.686 90 8 Suction-Side −1.788 −6.861 90 9 Suction-Side −1.294 −7.009 90 10 Suction-Side −0.794 −7.134 90 11 Suction-Side −0.288 −7.238 90 12 Suction-Side 0.220 −7.323 90 13 Suction-Side 0.731 −7.391 90 14 Suction-Side 1.244 −7.443 90 15 Suction-Side 1.759 −7.479 90 16 Suction-Side 2.274 −7.502 90 17 Suction-Side 2.790 −7.509 90 18 Suction-Side 3.305 −7.504 90 19 Suction-Side 3.821 −7.486 90 20 Suction-Side 4.335 −7.455 90 21 Suction-Side 4.849 −7.412 90 22 Suction-Side 5.362 −7.358 90 23 Suction-Side 5.874 −7.292 90 24 Suction-Side 6.384 −7.215 90 25 Suction-Side 6.892 −7.128 90 26 Suction-Side 7.398 −7.029 90 27 Suction-Side 7.902 −6.921 90 28 Suction-Side 8.404 −6.802 90 29 Suction-Side 8.903 −6.673 90 30 Suction-Side 9.400 −6.534 90 31 Suction-Side 9.894 −6.385 90 32 Suction-Side 10.385 −6.227 90 33 Suction-Side 10.872 −6.058 90 34 Suction-Side 11.356 −5.880 90 35 Suction-Side 11.836 −5.693 90 36 Suction-Side 12.313 −5.496 90 37 Suction-Side 12.785 −5.288 90 38 Suction-Side 13.254 −5.072 90 39 Suction-Side 13.717 −4.846 90 40 Suction-Side 14.176 −4.610 90 41 Suction-Side 14.630 −4.365 90 42 Suction-Side 15.078 −4.111 90 43 Suction-Side 15.521 −3.847 90 44 Suction-Side 15.959 −3.574 90 45 Suction-Side 16.391 −3.292 90 46 Suction-Side 16.817 −3.002 90 47 Suction-Side 17.237 −2.703 90 48 Suction-Side 17.651 −2.395 90 49 Suction-Side 18.059 −2.079 90 50 Suction-Side 18.460 −1.756 90 51 Suction-Side 18.856 −1.424 90 52 Suction-Side 19.244 −1.086 90 53 Suction-Side 19.627 −0.740 90 54 Suction-Side 20.004 −0.387 90 55 Suction-Side 20.374 −0.028 90 56 Suction-Side 20.738 0.337 90 57 Suction-Side 21.096 0.708 90 58 Suction-Side 21.448 1.085 90 59 Suction-Side 21.795 1.467 90 60 Suction-Side 22.136 1.854 90 61 Suction-Side 22.471 2.245 90 62 Suction-Side 22.801 7.647 90 63 Suction-Side 23.126 3.043 90 64 Suction-Side 23.445 3.447 90 65 Suction-Side 23.760 3.856 90 66 Suction-Side 24.071 4.267 90 67 Suction-Side 24.376 4.683 90 68 Suction-Side 24.678 5.101 90 69 Suction-Side 24.975 5.522 90 70 Suction-Side 25.269 5.946 90 71 Suction-Side 25.558 6.374 90 72 Suction-Side 25.844 6.803 90 73 Suction-Side 26.126 7.234 90 74 Suction-Side 26.405 7.668 90 75 Suction-Side 26.680 8.104 90 76 Suction-Side 26.953 8.542 90 77 Suction-Side 27.222 8.982 90 78 Suction-Side 27.489 9.423 90 79 Suction-Side 27.753 9.866 90 80 Suction-Side 28.015 10.311 90 81 Suction-Side 28.274 10.757 90 82 Suction-Side 28.531 11.204 90 83 Suction-Side 28.785 11.652 90 84 Suction-Side 29.038 12.102 90 85 Suction-Side 29.289 12.553 90 86 Suction-Side 29.538 13.004 90 87 Suction-Side 29.785 13.457 90 88 Suction-Side 30.030 13.910 90 89 Suction-Side 30.274 14.365 90 90 Suction-Side 30.517 14.820 90 91 Suction-Side 30.759 15.275 90 92 Suction-Side 30.999 15.732 90 93 Suction-Side 31.239 16.188 90 94 Suction-Side 31.478 16.646 90 95 Suction-Side 31.715 17.103 90 96 Suction-Side 31.952 17.561 90 97 Suction-Side 32.188 18.020 90 98 Suction-Side 32.424 18.479 90 99 Suction-Side 32.659 18.938 90 100 Suction-Side 32.893 19.397 90 101 Pressure-Side 32.851 19.834 90 102 Pressure-Side 32.507 19.599 90 103 Pressure-Side 32.254 19.213 90 104 Pressure-Side 31.998 18.828 90 105 Pressure-Side 31.740 18.445 90 106 Pressure-Side 31.479 18.064 90 107 Pressure-Side 31.215 17.685 90 108 Pressure-Side 30.948 17.309 90 109 Pressure-Side 30.677 16.934 90 110 Pressure-Side 30.403 16.562 90 111 Pressure-Side 30.127 16.193 90 112 Pressure-Side 29.846 15.826 90 113 Pressure-Side 29.563 15.461 90 114 Pressure-Side 29.275 15.100 90 115 Pressure-Side 28.984 14.741 90 116 Pressure-Side 28.690 14.385 90 117 Pressure-Side 28.391 14.033 90 118 Pressure-Side 28.089 13.684 90 119 Pressure-Side 27.783 13.338 90 120 Pressure-Side 27.472 12.996 90 121 Pressure-Side 27.158 12.658 90 122 Pressure-Side 26.840 12.323 90 123 Pressure-Side 26.517 11.993 90 124 Pressure-Side 26.191 11.666 90 125 Pressure-Side 25.860 11.343 90 126 Pressure-Side 25.525 11.025 90 127 Pressure-Side 25.187 10.711 90 128 Pressure-Side 24.844 10.402 90 129 Pressure-Side 24.497 10.097 90 130 Pressure-Side 24.146 9.796 90 131 Pressure-Side 23.791 9.501 90 132 Pressure-Side 23.433 9.210 90 133 Pressure-Side 23.070 8.923 90 134 Pressure-Side 22.704 8.642 90 135 Pressure-Side 22.335 8.365 90 136 Pressure-Side 21.962 8.092 90 137 Pressure-Side 21.585 7.825 90 138 Pressure-Side 21.205 7.562 90 139 Pressure-Side 20.822 7.304 90 140 Pressure-Side 20.436 7.051 90 141 Pressure-Side 20.047 6.802 90 142 Pressure-Side 19.655 6.558 90 143 Pressure-Side 19.260 6.319 90 144 Pressure-Side 18.862 6.084 90 145 Pressure-Side 18.462 5.854 90 146 Pressure-Side 18.059 5.628 90 147 Pressure-Side 17.654 5.406 90 148 Pressure-Side 17.246 5.189 90 149 Pressure-Side 16.836 4.977 90 150 Pressure-Side 16.424 4.768 90 151 Pressure-Side 16.010 4.564 90 152 Pressure-Side 15.594 4.364 90 153 Pressure-Side 15.175 4.168 90 154 Pressure-Side 14.755 3.976 90 155 Pressure-Side 14.333 3.789 90 156 Pressure-Side 13.909 3.605 90 157 Pressure-Side 13.484 3.426 90 158 Pressure-Side 13.057 3.250 90 159 Pressure-Side 12.628 3.077 90 160 Pressure-Side 12.198 2.909 90 161 Pressure-Side 11.767 2.744 90 162 Pressure-Side 11.334 2.583 90 163 Pressure-Side 10.900 2.425 90 164 Pressure-Side 10.465 2.270 90 165 Pressure-Side 10.028 2.119 90 166 Pressure-Side 9.591 1.970 90 167 Pressure-Side 9.153 1.825 90 168 Pressure-Side 8.714 1.682 90 169 Pressure-Side 8.273 1.542 90 170 Pressure-Side 7.833 1.405 90 171 Pressure-Side 7.391 1.269 90 172 Pressure-Side 6.949 1.136 90 173 Pressure-Side 6.506 1.004 90 174 Pressure-Side 6.063 0.874 90 175 Pressure-Side 5.620 0.745 90 176 Pressure-Side 5.176 0.617 90 177 Pressure-Side 4.732 0.490 90 178 Pressure-Side 4.288 0.362 90 179 Pressure-Side 3.844 0.235 90 180 Pressure-Side 3.400 0.107 90 181 Pressure-Side 2.956 −0.021 90 182 Pressure-Side 2.513 −0.151 90 183 Pressure-Side 2.071 −0.283 90 184 Pressure-Side 1.629 −0.418 90 185 Pressure-Side 1.188 −0.555 90 186 Pressure-Side 0.748 −0.697 90 187 Pressure-Side 0.310 −0.843 90 188 Pressure-Side −0.126 −0.995 90 189 Pressure-Side −0.560 −1.153 90 190 Pressure-Side −0.990 −1.320 90 191 Pressure-Side −1.417 −1.497 90 192 Pressure-Side −1.838 −1.687 90 193 Pressure-Side −2.251 −1.893 90 194 Pressure-Side −2.655 −2.117 90 195 Pressure-Side −3.044 −2.365 90 196 Pressure-Side −3.412 −2.644 90 197 Pressure-Side −3.748 −2.960 90 198 Pressure-Side −4.035 −3.322 90 199 Pressure-Side −4.249 −3.730 90 200 Pressure-Side −4.367 −4.176 90 1 Suction-Side −4.856 −5.150 100 2 Suction-Side −4.729 −5.659 100 3 Suction-Side −4.444 −6.100 100 4 Suction-Side −4.055 −6.456 100 5 Suction-Side −3.610 −6.738 100 6 Suction-Side −3.134 −6.965 100 7 Suction-Side −2.640 −7.150 100 8 Suction-Side −2.135 −7.302 100 9 Suction-Side −1.623 −7.427 100 10 Suction-Side −1.106 −7.531 100 11 Suction-Side −0.586 −7.617 100 12 Suction-Side −0.063 −7.687 100 13 Suction-Side 0.462 −7.742 100 14 Suction-Side 0.988 −7.785 100 15 Suction-Side 1.514 −7.815 100 16 Suction-Side 2.041 −7.834 100 17 Suction-Side 2.568 −7.841 100 18 Suction-Side 3.096 −7.839 100 19 Suction-Side 3.623 −7.825 100 20 Suction-Side 4.150 −7.801 100 21 Suction-Side 4.676 −7.767 100 22 Suction-Side 5.202 −7.722 100 23 Suction-Side 5.726 −7.667 100 24 Suction-Side 6.250 −7.601 100 25 Suction-Side 6.772 −7.525 100 26 Suction-Side 7.292 −7.439 100 27 Suction-Side 7.811 −7.342 100 28 Suction-Side 8.327 −7.236 100 29 Suction-Side 8.842 −7.118 100 30 Suction-Side 9.353 −6.991 100 31 Suction-Side 9.862 −6.853 100 32 Suction-Side 10.369 −6.705 100 33 Suction-Side 10.872 −6.546 100 34 Suction-Side 11.372 −6.378 100 35 Suction-Side 11.868 −6.200 100 36 Suction-Side 12.361 −6.012 100 37 Suction-Side 12.850 −5.814 100 38 Suction-Side 13.334 −5.606 100 39 Suction-Side 13.815 −5.388 100 40 Suction-Side 14.291 −5.160 100 41 Suction-Side 14.762 −4.923 100 42 Suction-Side 15.228 −4.676 100 43 Suction-Side 15.689 −4.420 100 44 Suction-Side 16.144 −4.154 100 45 Suction-Side 16.594 −3.879 100 46 Suction-Side 17.038 −3.595 100 47 Suction-Side 17.477 −3.301 100 48 Suction-Side 17.909 −2.999 100 49 Suction-Side 18.335 −2.687 100 50 Suction-Side 18.754 −2.367 100 51 Suction-Side 19.166 −2.038 100 52 Suction-Side 19.572 −1.701 100 53 Suction-Side 19.971 −1.357 100 54 Suction-Side 20.363 −1.004 100 55 Suction-Side 20.748 −0.644 100 56 Suction-Side 21.127 −0.276 100 57 Suction-Side 21.499 0.098 100 58 Suction-Side 21.864 0.479 100 59 Suction-Side 22.222 0.865 100 60 Suction-Side 22.574 1.258 100 61 Suction-Side 22.920 1.657 100 62 Suction-Side 23.260 2.060 100 63 Suction-Side 23.594 2.468 100 64 Suction-Side 23.922 2.881 100 65 Suction-Side 24.245 3.298 100 66 Suction-Side 24.563 3.719 100 67 Suction-Side 24.876 4.144 100 68 Suction-Side 25.184 4.572 100 69 Suction-Side 25.487 5.003 100 70 Suction-Side 25.787 5.437 100 71 Suction-Side 26.082 5.875 100 72 Suction-Side 26.373 6.314 100 73 Suction-Side 26.661 6.757 100 74 Suction-Side 26.944 7.201 100 75 Suction-Side 27.225 7.648 100 76 Suction-Side 27.502 8.096 100 77 Suction-Side 27.777 8.547 100 78 Suction-Side 28.049 8.999 100 79 Suction-Side 28.317 9.453 100 80 Suction-Side 28.584 9.908 100 81 Suction-Side 28.847 10.365 100 82 Suction-Side 29.109 10.823 100 83 Suction-Side 29.368 11.282 100 84 Suction-Side 29.625 11.743 100 85 Suction-Side 29.879 12.205 100 86 Suction-Side 30.132 12.668 100 87 Suction-Side 30.383 13.132 100 88 Suction-Side 30.633 13.597 100 89 Suction-Side 30.880 14.063 100 90 Suction-Side 31.126 14.529 100 91 Suction-Side 31.371 14.996 100 92 Suction-Side 31.614 15.464 100 93 Suction-Side 31.855 15.933 100 94 Suction-Side 32.096 16.403 100 95 Suction-Side 32.335 16.873 100 96 Suction-Side 32.574 17.343 100 97 Suction-Side 32.811 17.814 100 98 Suction-Side 33.048 18.286 100 99 Suction-Side 33.284 18.757 100 100 Suction-Side 33.520 19.229 100 101 Pressure-Side 33.473 19.679 100 102 Pressure-Side 33.125 19.431 100 103 Pressure-Side 32.869 19.033 100 104 Pressure-Side 32.610 18.637 100 105 Pressure-Side 32.347 18.243 100 106 Pressure-Side 32.082 17.852 100 107 Pressure-Side 31.812 17.463 100 108 Pressure-Side 31.539 17.077 100 109 Pressure-Side 31.262 16.693 100 110 Pressure-Side 30.980 16.313 100 111 Pressure-Side 30.695 15.936 100 112 Pressure-Side 30.405 15.562 100 113 Pressure-Side 30.112 15.190 100 114 Pressure-Side 29.814 14.823 100 115 Pressure-Side 29.512 14.459 100 116 Pressure-Side 29.205 14.099 100 117 Pressure-Side 28.894 13.742 100 118 Pressure-Side 28.578 13.390 100 119 Pressure-Side 28.258 13.041 100 120 Pressure-Side 27.934 12.697 100 121 Pressure-Side 27.604 12.357 100 122 Pressure-Side 27.271 12.022 100 123 Pressure-Side 26.933 11.691 100 124 Pressure-Side 26.590 11.364 100 125 Pressure-Side 26.243 11.043 100 126 Pressure-Side 25.892 10.726 100 127 Pressure-Side 25.537 10.413 100 128 Pressure-Side 25.177 10.106 100 129 Pressure-Side 24.813 9.803 100 130 Pressure-Side 24.446 9.506 100 131 Pressure-Side 24.074 9.213 100 132 Pressure-Side 23.698 8.925 100 133 Pressure-Side 23.319 8.642 100 134 Pressure-Side 22.936 8.364 100 135 Pressure-Side 22.550 8.091 100 136 Pressure-Side 22.160 7.823 100 137 Pressure-Side 21.767 7.560 100 138 Pressure-Side 21.370 7.302 100 139 Pressure-Side 20.971 7.049 100 140 Pressure-Side 20.568 6.801 100 141 Pressure-Side 20.162 6.557 100 142 Pressure-Side 19.753 6.318 100 143 Pressure-Side 19.342 6.084 100 144 Pressure-Side 18.928 5.855 100 145 Pressure-Side 18.512 5.631 100 146 Pressure-Side 18.093 5.411 100 147 Pressure-Side 17.672 5.195 100 148 Pressure-Side 17.248 4.985 100 149 Pressure-Side 16.823 4.778 100 150 Pressure-Side 16.395 4.576 100 151 Pressure-Side 15.965 4.378 100 152 Pressure-Side 15.534 4.184 100 153 Pressure-Side 15.100 3.993 100 154 Pressure-Side 14.665 3.807 100 155 Pressure-Side 14.229 3.625 100 156 Pressure-Side 13.791 3.446 100 157 Pressure-Side 13.352 3.270 100 158 Pressure-Side 12.911 3.098 100 159 Pressure-Side 12.469 2.929 100 160 Pressure-Side 12.026 2.764 100 161 Pressure-Side 11.582 2.601 100 162 Pressure-Side 11.136 2.440 100 163 Pressure-Side 10.690 2.283 100 164 Pressure-Side 10.243 2.128 100 165 Pressure-Side 9.795 1.975 100 166 Pressure-Side 9.347 1.824 100 167 Pressure-Side 8.898 1.676 100 168 Pressure-Side 8.448 1.529 100 169 Pressure-Side 7.998 1.384 100 170 Pressure-Side 7.547 1.241 100 171 Pressure-Side 7.095 1.098 100 172 Pressure-Side 6.644 0.958 100 173 Pressure-Side 6.192 0.818 100 174 Pressure-Side 5.739 0.679 100 175 Pressure-Side 5.287 0.541 100 176 Pressure-Side 4.834 0.403 100 177 Pressure-Side 4.381 0.266 100 178 Pressure-Side 3.929 0.129 100 179 Pressure-Side 3.476 −0.009 100 180 Pressure-Side 3.023 −0.147 100 181 Pressure-Side 2.571 −0.286 100 182 Pressure-Side 2.119 −0.426 100 183 Pressure-Side 1.668 −0.568 100 184 Pressure-Side 1.217 −0.713 100 185 Pressure-Side 0.768 −0.860 100 186 Pressure-Side 0.320 −1.012 100 187 Pressure-Side −0.127 −1.168 100 188 Pressure-Side −0.571 −1.330 100 189 Pressure-Side −1.013 −1.499 100 190 Pressure-Side −1.452 −1.677 100 191 Pressure-Side −1.885 −1.866 100 192 Pressure-Side −2.313 −2.068 100 193 Pressure-Side −2.733 −2.287 100 194 Pressure-Side −3.141 −2.526 100 195 Pressure-Side −3.533 −2.790 100 196 Pressure-Side −3.903 −3.086 100 197 Pressure-Side −4.238 −3.419 100 198 Pressure-Side −4.522 −3.797 100 199 Pressure-Side −4.732 −4.220 100 200 Pressure-Side −4.847 −4.678 100

It will also be appreciated that the airfoil 250 disclosed in the above Table 1 may be scaled up or down geometrically for use in other similar turbine designs. Consequently, the coordinate values set forth in Table 1 may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in Table 1 would be represented by X, Y and Z coordinate values of Table 1, with the X, Y and Z non-dimensional coordinate values converted to inches, multiplied or divided by a constant number.

An important term in this disclosure is profile. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in Table 1. The actual profile on a manufactured blade will be different than those in Table 1 and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. The airfoil shape provides a unique profile to achieve (1) interaction between other stages in the high pressure turbine; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings. The disclosed loci of points allow the gas turbine or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as (1) interaction between other stages in the high pressure turbine; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled turbine.

The airfoil 250 described herein thus improves overall gas turbine 100 efficiency. Specifically, the airfoil 250 provides the desired turbine efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 250 also meets all aeromechanics and stress requirements.

The nozzle 220 described herein has very specific aerodynamic design requirements such as an upstream bucket radial back pressure (i.e., work splits) and radial velocity triangles for the downstream bucket. Significant cross-functional design effort was require to meet these design goals. The airfoil 250 of the nozzle 220 thus is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost effective manner.

It should be apparent that the foregoing relates only to certain embodiments of the present application and the resultant patent. Numerous changes and modifications may be made herein by one of ordinary skill in the art without departing from the general spirit and scope of the invention as defined by the following claims and the equivalents thereof. 

We claim:
 1. A turbine nozzle comprising an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1 wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each distance Z, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
 2. The turbine nozzle of claim 1, wherein the turbine nozzle comprises a stage nozzle of a turbine.
 3. The turbine nozzle of claim 1, wherein the turbine nozzle forms part of a stage of a turbine.
 4. The turbine nozzle of claim 1, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 5. The turbine nozzle of claim 1, wherein a height of the turbine nozzle is about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters) in length.
 6. The turbine nozzle of claim 1, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 7. A turbine nozzle comprising a nozzle airfoil having a suction-side uncoated nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table 1 wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at the Z distances being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y and Z distances being scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 8. The turbine nozzle of claim 7, wherein the turbine nozzle comprises a stage nozzle of a turbine.
 9. The turbine nozzle of claim 7, wherein the turbine nozzle forms part of a stage of a turbine.
 10. The turbine nozzle of claim 7, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 11. The turbine nozzle of claim 7, wherein a height of the turbine nozzle is about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters) in length.
 12. A turbine comprising a plurality of nozzles, each of the nozzles comprising an airfoil having an airfoil shape, the airfoil having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table 1 wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances in inches by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in inches, and wherein X and Y are distances in inches which, when connected by smooth continuing arcs, define airfoil profile sections at each Z distance, the airfoil profile sections at Z distances being joined smoothly with one another to form a complete airfoil shape.
 13. The turbine of claim 12, wherein the plurality of nozzles comprises a plurality of stage nozzles of the turbine.
 14. The turbine of claim 12, wherein the plurality of nozzles forms part of a stage of a turbine.
 15. The turbine of claim 12, wherein the airfoil shape lies in an envelope within at least one of +/−5% and/or +/−5% of a chord length in a direction normal to any airfoil surface location.
 16. The turbine of claim 12, wherein a height the turbine nozzle is about 5 inches to about 50 inches (about 12 centimeters to about 130 centimeters) in length.
 17. The turbine of claim 12, wherein the X, Y and Z distances are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 18. The turbine of claim 12, wherein X represents a distance parallel to a turbine axis of rotation. 